Glass sheets are commonly used, for example, in display applications, for example liquid crystal displays (LCDs), electrophoretic displays (EPD), organic light emitting diode displays (OLEDs), plasma display panels (PDPs), or the like. Glass sheets are commonly fabricated by flowing molten glass to a forming body whereby a glass ribbon may be formed by a variety of ribbon forming process techniques, for example, slot draw, float, down-draw, fusion down-draw, or up-draw. The glass ribbon may then be subsequently divided to provide sheet glass suitable for further processing into a desired display or other application. Nowadays there is a growing interest for extremely high quality thin glass sheets with 3D shapes, and in particular with a combination of flat portions and locally highly curved shapes, for use in display devices or other applications. Thus, there is a need for a process and apparatus which allow: retention of a high level of flatness in the desired areas, usually by far the largest area; retention of the pristine aspect of the glass sheets; desired amount of deformation in the areas of interest; and a high level of dimensional control. Such process and apparatus can be suitable for reforming glass sheets in a wide range of applications incorporating glass sheets such as appliances (e.g. display applications) or other devices incorporating a reformed glass sheet.